Autocorrelation

Definition

Autocorrelation (serial correlation or lagged correlation) measures how similar a time series is to a lagged version of itself. It quantifies the relationship between observations at different time points: a positive autocorrelation means past values tend to be followed by similar values; a negative autocorrelation means past values tend to be followed by opposite values. The autocorrelation coefficient ranges from −1 to +1.

How it works

Compute the correlation between the series and the same series shifted by a given lag (one period, two periods, etc.).
Values near +1 indicate a strong positive linear relationship across the lag; values near −1 indicate a strong negative linear relationship; values near 0 indicate weak linear dependence.
Autocorrelation primarily detects linear dependence; small autocorrelation does not rule out nonlinear relationships.

Interpreting values

+1: perfect positive serial correlation (past increases → future increases).
−1: perfect negative serial correlation (past increases → future decreases).
0: no linear serial correlation.
Look at multiple lags (lag 1, lag 2, …) to understand persistence and seasonality.

Common tests and diagnostics

Durbin–Watson test: popular in regression settings. Produces a statistic between 0 and 4:
Near 0: strong positive autocorrelation.
Near 2: little or no autocorrelation.
Near 4: strong negative autocorrelation.
Autocorrelation function (ACF) plots: visualize autocorrelation across many lags.
Partial autocorrelation function (PACF) plots: useful to identify the appropriate lag order in autoregressive models.

Why autocorrelation matters

Many statistical methods assume independent observations; autocorrelation violates this assumption.
In regression, serially correlated residuals can lead to biased standard errors and invalid hypothesis tests.
In time-series modeling and forecasting, identifying autocorrelation is essential to choose appropriate models (e.g., AR, MA, ARIMA).

Applications in finance and technical analysis

Traders and analysts use autocorrelation to assess predictability of returns and the presence of momentum.
A positive lag-1 autocorrelation suggests short-term continuation (momentum); negative suggests mean reversion.
Autocorrelation is typically combined with other tools and statistical measures for robust decision-making.

Practical example

Suppose a trader finds a stock’s lag‑1 return has an autocorrelation of 0.8. Because 0.8 is close to +1, past returns are strong positive predictors of next-period returns. The trader might treat the stock as exhibiting momentum and adjust positions accordingly (e.g., hold or accumulate after gains). Such decisions should still consider transaction costs, risk management, and confirmation from other analyses.